THE ANISOTROPIC ELASTIC SEMIINFINITE STRIP

It is known that the stresses of an isotropic elastic semi-infinite strip decay exponentially at large distance x1 from the end x1 = 0 if the sides x2 = +/-1 are traction free and the loading at x1 = 0 is in self-equilibrium. We study the associated problem for a general anisotropic elastic strip. Eight different side conditions at x2 = +/-1 and eight different end conditions at x1 = 0 are considered. With the Stroh formalism, all these different side and end conditions are encompassed in one simple formulation. It is shown that, for certain side conditions, the loading at x1 = 0 need not be in self-equilibrium. The decay factor for the strip of monoclinic materials with the plane of symmetry at x3 = 0 and with the sides x2 = +/-1 being traction free is derived, and it has a remarkably simple expression. Numerical calculations of the smallest decay factor are presented.